H∞ Filtering For Discrete-time Singular Markov Jump Systems With Time-varying Delay

This paper considers H∞filter design for a class of discrete-time singular Markov jump system with norm-bounded and time-varying delay based on a delay decomposition approach.In the method, the variation interval of the time delay is divided into two subintervals. By considering the variation of the Lyapunov functional in every subinterval, the H∞filter design problem is solved.Let the system dynamics be described by the following: where xk E Rn is the state of the system, yk∈Rm is measured output, zk∈Rq is the signal to be estimated,wk∈R9 is the disturbance input that belongs to l2[0,∞). dk is a time-varying delay satisfying 0<d1≤dk≤d2, where d1 and d2 are prescribed positive integers.φ(k) is the compatible initial condition. {rk,k≥0} is a Markov chain taking values in finite space (?)=﹛1,2,….N} with transition probability from mode i at time k to mode j at time k+1 The matrix E∈RnXn may be singular and it is assumed that rank (E)=r< n, for each rk∈(?), we have where A(rk), Ad{rk),C(rk),Cd(rk), L(rk) are known constant matrices with ap-propriate dimensions.δA(rk),δAd(rk),σC(rk),σCd(rk) are unknown matrices with norm-bounded. The purpose of this paper is to design a filter in the following form:such that the dynamics error system which composed by system (1) and filter (3) is regular, casual, stochastically stable with disturbance attenuation levelΥThe paper is organized as following:The first chapter introduces the current research of singular system and singular Markov systems.In chapter two, based on restricted system equivalent transformation and constructing a new state vector, the system (1) is transformed into a standard discrete Markov jump system,and the equivalence of the H∞, filtering problem for the two systems is demonstrated. Hence we can discuss the H^, filtering problem for the standard discrete Markov jump system instead of that for system (1).In chapter three, by constructing a Lyapunov function based on a piece-wise analysis method, a sufficient condition which makes standard Markov jump system to be stable is given.In chapter four,based on the results given in chapter three, the design of H∞filter is discussed.An LMI sufficient condition for the existence of H∞filter is given and the filter parameter matrices are also presented.In chapter five,a numerical example is provided to illustrate the effective-ness of the method.